25x^2+2x=1500

Solution for 25x^2+2x=1500 equation:

25x^2+2x=1500

We move all terms to the left:

25x^2+2x-(1500)=0

a = 25; b = 2; c = -1500;
Δ = b2-4ac
Δ = 22-4·25·(-1500)
Δ = 150004
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{150004}=\sqrt{4*37501}=\sqrt{4}*\sqrt{37501}=2\sqrt{37501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{37501}}{2*25}=\frac{-2-2\sqrt{37501}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{37501}}{2*25}=\frac{-2+2\sqrt{37501}}{50}
$